We could cast doubt on even making the distinction between economic and conventional warfare, as there are so many overlapping relationships between them that they often bleed into each other spatially and temporally. A more useful distinction for long term analysis might be forms of soft power and hard power, with the latter coming up out of necessity when the former is not present or is exhausted. Indeed, soft power is often the preferred channel for a hegemon grown comfortable with its status, often becoming addicted to the exercise of that power long after its hard backing stores are used up.
What even is an economic society, or a military society in the first place? Why does it come about? Is the distinction truly significant?
Nevertheless, in a large complex society there does seem to be differentiated economic and military spheres, in which more specialized individuals reside which excel at one sphere over the other, and so at present we're making use of these contrasting sites to further the analysis.
The terminology is by no means fixed at present, and could be considered interchangeable depending on the illumination or the point being made. We can see what proves more useful.